I would say you're pretty close. I think you need the equivalent of a "normal" force that is perpendicular to the angled thread. It gets pretty hard to get your head around the helical screw thread, so I did a quick analysis of a much simpler screw, which consists of a bolt with a small post that acts as the thread and a hole with a helical groove cut in it.
The results of the free body diagram confirm the result you get from a "work balance" analysis:
Fvert = 2*pi*T/d
Where Fvert is the vertical force, T is the applied torque, and d is the thread pitch.
This analysis ignores friction, which is a huge simplification. Hope this helps...